High-pressure single-crystal X-ray diffraction experiments were conducted on natural cordierite crystals with composition Mg1.907(18)Fe0.127(6)Al4.01(2)Si4.96(3)Na0.026(3)O18.12(9) using a synchrotron X-ray source. The samples were compressed at 300 K in a diamond-anvil cell to a maximum pressure of 15.22(15) GPa with a neon pressure-transmitting medium and a gold pressure calibrant. We observed a recently described orthorhombic to phase transition, as well as a further transition to a second triclinic phase. We solved and refined both new triclinic phases in space group P1, and designate them cordierite II and III. The structures of cordierite II and III were refined at 7.52(3) and 15.22(15) GPa, respectively. The lattice parameters at these pressures are a = 15.567(3), b = 9.6235(4), c = 9.0658(6) Å, α = 89.963(5)°, β = 86.252(10)°, and γ = 90.974(8)° for cordierite II, and a = 8.5191(19), b = 8.2448(3), c = 9.1627(4) Å, α = 85.672(4)°, β = 85.986(7)°, and γ = 70.839(10)° for cordierite III. Across the phase transitions there is a significant reduction in the length of the a-axis (~2 Å per phase transition), whereas both the b- and c-axis remain largely unchanged. Cordierite II has fourfold- and fivefold-coordinated Si and Al, while cordierite III has fourfold-, fivefold-, and sixfold-coordinated Si, fourfold- and fivefold-coordinated Al, and fivefold- and sixfold-coordinated Mg. The sequence of high-pressure phases shows increasing polymerization of coordination polyhedra. These results, together with other recent studies, suggest that mixed four-, five-, and sixfold coordination states may occur more commonly in silicate structures compressed at 300 K than previously recognized.